Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
332 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C16×D67 | C2 | semidirect |
| 3. #22558971 | C2 | semidirect |
| 4. #22558174 | C2 | semidirect |
| 5. #22558172 | C2 | semidirect |
| 6. #22558170 | C2 | semidirect |
| 7. C67×#1331 | C2 | semidirect |
| 160. #1331 | D67 | semidirect |
| 161. C67 | #11673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570777 | 2 |
| C4×C16×D67 | 2 |
| #22558971 | 2 |
| #22558174 | 2 |
| #22558172 | 2 |
| #22558170 | 2 |
| C67×#1331 | 2 |
| #11673 | 67 |